Dan and Karen, who live 10 miles apart meet at a cafe that is directly north
of Dan's house and directly east of Karen's house. If the cafe is 2 miles closer to Dan's house than to karen's house, how many miles is the cafe from Karen's house?
A 6
B 7
C 8
D 9
E 10
OA is C
coordinates? word problem...from gmat prep
This topic has expert replies
Cafe is closer to Dan's house by 2 miles. so if distance between cafe and karen's house is x, then distance between cafe and Dan's house is x2.
(Karen)(X)(Cafe)
\ 
\ 
\ 
(10) (x2)
\ 
\ 
\ 
(Dan)
Its a Right angle triangle, so using Pyto therom.
x^2 + (x2)^2 = 10^2
the equation can be then solved to get the values of 2 sides as 6 and 8. cafe is closer the Dan's house than Karen's, hence distace between cafe and laren's house is 8.
(Karen)(X)(Cafe)
\ 
\ 
\ 
(10) (x2)
\ 
\ 
\ 
(Dan)
Its a Right angle triangle, so using Pyto therom.
x^2 + (x2)^2 = 10^2
the equation can be then solved to get the values of 2 sides as 6 and 8. cafe is closer the Dan's house than Karen's, hence distace between cafe and laren's house is 8.
GMAT/MBA Expert
 lunarpower
 GMAT Instructor
 Posts: 3380
 Joined: 03 Mar 2008
 Thanked: 2256 times
 Followed by:1530 members
 GMAT Score:800
well played.sxjain3 wrote:Cafe is closer to Dan's house by 2 miles. so if distance between cafe and karen's house is x, then distance between cafe and Dan's house is x2.
(Karen)(X)(Cafe)
\ 
\ 
\ 
(10) (x2)
\ 
\ 
\ 
(Dan)
Its a Right angle triangle, so using Pyto therom.
x^2 + (x2)^2 = 10^2
the equation can be then solved to get the values of 2 sides as 6 and 8. cafe is closer the Dan's house than Karen's, hence distace between cafe and laren's house is 8.

IMPORTANT BACKGROUND INFORMATION
this is the point at which i come on stage, waving a flag and yelling the following incantation:
memorize the famous pythagorean triples.
these are the ones i call 'celebrity triangles', because they look nice and pop up all over the place:
345 and 51213 are the 'alist celebrity triangles'
81517 and 72425 are the 'blist celebrity triangles'
the 'alist' triangles, just like actual alist celebrities, pop up in different forms so they're harder to recognize.** so in other words, not only should you look for 345 triangles, but also 6810 triangles, 91215 triangles, etc. also, in addition to 51213, you should keep an eye out for 102426 triangles.
in addition, the alist triangles have impostors;** if you see a right triangle with a 3 and a 5 on it, for example, make sure that the 3 is a leg and the 5 is the hypotenuse. if the 3 and 5 are legs, then the hypotenuse is √34, not 4.
the 'blist' triangles (again just like the corresponding celebrities), because they're more obscure, can walk around in public because not very many people recognize them. in other words, if you see an 81517 triangle, then the side lengths will probably be actually 8, actually 15, and actually 17. same goes for the 72425 (and the clist triangles like 94041 and 202129, if you're really hardcore).

if you're familiar with the backgroud information above, then you can solve this problem in less than half a minute (depending on drawing speed), using the following reasoning:
* draw it
* hey look, i need a hypotenuse of 10 and legs that differ by 2
* let me search my mental inventory of celebrity triangles
* 6810!
* done.

**this is probably the best analogy i've ever concocted in my life.
Ron has been teaching various standardized tests for 20 years.

Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions Ã Ron en franÃ§ais
Voit esittÃ¤Ã¤ kysymyksiÃ¤ Ron:lle myÃ¶s suomeksi

Quand on se sent bien dans un vÃªtement, tout peut arriver. Un bon vÃªtement, c'est un passeport pour le bonheur.
Yves SaintLaurent

Learn more about ron

Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions Ã Ron en franÃ§ais
Voit esittÃ¤Ã¤ kysymyksiÃ¤ Ron:lle myÃ¶s suomeksi

Quand on se sent bien dans un vÃªtement, tout peut arriver. Un bon vÃªtement, c'est un passeport pour le bonheur.
Yves SaintLaurent

Learn more about ron
I guess drawing the figure right will make this Q simpler or harder
The correct figure should be. Note that D should be directly below C and is not being rendered properly. Probably what happened with the other poster.
X
KC

 X2





D
The correct figure should be. Note that D should be directly below C and is not being rendered properly. Probably what happened with the other poster.
X
KC

 X2





D